A plate cylinder of the aforementioned type is known from U.S. Pat. No. 5,284,093. In a receiving gap in the plate cylinder, a clamping element of a clamping device is arranged displaceably in order to fasten a printing plate on the outer surface of the plate cylinder by clamping the regions of the starting and ending edges of the printing plate. For this purpose, the regions of the starting and end edges of the printing plate are bent in approximately a radial direction and extend into a clamping-slot space, the clamping being effected by corresponding displacement of the clamping element of the clamping device. In its loosened condition, the clamping element extends beyond the periphery of the outer surface of the printing-plate cylinder. When the clamping process takes place, the clamping element moves along the radial direction into the receiving gap, the clamping element in the clamped condition being more or less flush with the rest of the surface of the plate cylinder, depending on the clamp end position and the thickness of the printing plate used. If a relatively short printing plate is used, the clamping element may extend outward beyond the outer surface of the plate cylinder in the clamped condition. With a printing plate which is somewhat longer than the normal size, the clamping element may move so far into the plate cylinder that its surface is lower than the resting surface of the plate cylinder. Furthermore, the clamping force and also the dimensional accuracy of spring elements which are used to clamp the regions of the starting and end edges of the printing plate determine what position the clamping element in the firmly clamped condition assumes relative to the outer surface of the plate cylinder. There is thus no assurance that the clamping element will be flush with the outer surface of the plate cylinder, resulting in uneven travel of the plate cylinder. This can lead to smearing or other undesireable effects during printing.